The invention relates to a method and apparatus for determining the degree of polarisation of nuclear spin polarised gases, in particular 3He or 129Xe.
Nuclear spin polarised gases, such as the helium isotope with mass number 3 (3He) or the isotope of xenon with mass number 129 (129Xe) and gases containing the fluorine, carbon or phosphorus isotopes 19F, 13C or 31P, are required for a wide variety of basic physics research experiments.
In the medical field, such isotopes have particularly been discussed for use in nuclear spin tomography (magnetic resonance imaging), for example of the lung. (See for example WO95/27438, WO97/37239, Bachert et al., Mag. Res. Med. 36: 192-196 (1996) and Ebert et al., The Lancet 347: 1297-1299 (1996)). In addition, Noxc3xal et al., J. Phys. III France 6: 1127-1132 (1996) discloses a 4He magnetometer used to detect the static magnetic field produced by optically pumped 3He nuclei submitted to RF discharge. Similarly, Cohen-Tannoudji et al., Phys. Rev. Letts. 22: 758-760 (1969) discloses the use of a sensitive low-field magnetometer to detect the static magnetic field produced by optically pumped 3He nuclei in a vapor. To be useful in nuclear spin tomography, the nuclear spin polarised gases require a degree of polarisation P of spin I of the atomic nucleus, or the nuclear magnetic dipole moment xcexcI connected therewith, which is about 4-5 orders of magnitude larger than PBoltzman the degree of polarisation of the gas in its relaxed state in normal thermal equilibrium in the magnetic field BT of the mr imaging apparatus. PBoltzmann is related to the Boltzmann constant, the magnetic dipole energy xe2x88x92xcexcIBT and thermal energy kT by:
xe2x80x83PBoltzmann=tan h(xcexcIBT/kT)xe2x80x83xe2x80x83(1)
(where k=Boltzmann constant, and T=absolute temperature in Kelvin).
Where PBoltzmann  less than  less than 1, then it approximates to xcexcI BT/kT.
Since routinely BT=1.5T and T=300K for the hydrogen isotope 1H used in tissue tomography, it has a PBoltzmann of only 5xc3x9710xe2x88x926, but in gas tomography a P greater than 1xc3x9710xe2x88x922 (i.e. 1%) is required. The requirement for such an extremely high P is mainly due to the low concentration of gas atoms in comparison to that of hydrogen in tissue. Gases with such degrees of polarisation (normally referred to as xe2x80x9chyperpolarised gasesxe2x80x9d) can be prepared using various known methods, advantageously by optical pumping or by polarization transfer.
In addition, large amounts of hyperpolarised gas, for example of the size of an intake of breath (0.5 to 1 litre) must be prepared for use.
Particularly high degrees of polarisationxe2x80x94for example  greater than 30%xe2x80x94in simultaneously high production amounts, for example 0.5 liters/h, may be achieved by compression of an optically pumped gas. This method is described in the following publications:
Eckert et al., Nuclear Instruments and Methods in Physics Research A 320: 53-65 (1992);
Becker et al., J. Neutron Research 5: 1-10 (1996);
Surkau et al., Nuclear Instruments and Methods in Physics Research A 384: 444-450 (1997); and
Heil et al., Physics Letters A 201: 337-343 (1995).
The extremely costly production of hyperpolarised gases, for example using the methods described above, generally involves production at a site remote from the place of use. As a result, they must be transported from the place of production to the user. Since a wide variety of relaxation processes (e.g. wall relaxation, relaxation in inhomogeneous, external, stray magnetic fields, etc.) causes the gas to depolarise to a greater or lesser extent, it is necessary to determine the degree of polarisation before using the hyperpolarised gas, for example in medical imaging.
One problem is that this must be determined as precisely as possible despite stray fields or applied fields. Further, the determination should be performable by relatively inexperienced personnel, ie. personnel who are not experts in the physics of hyperpolarized gases.
The present invention solves the above problem by providing a method for determining the degree of polarisation of nuclear spin polarised gases by exploiting the fact that nuclear spin polarisation of gases produces magnetic fields Bd in the nanoTesla to microTesla (nT to xcexcT) range.
Thus viewed from one aspect the invention provides a method of determining the degree of polarisation (P) of a nuclear spin polarised gas in a container, said method comprising determining the magnetic field Bd of the polarised gas using a magnetic field sensor and then determining therefrom the degree of polarisation of the gas.
In the method of the invention, the shape and size of the container into which the polarised gas is placed is important. Thus, the magnetic field Bd, which is dependent on the degree of polarisation of the gases, may be determined using a magnetic field sensor, e.g. a magnetometer, rather than a nuclear magnetic resonance polarimeter as has been used in the past, and the absolute degree of polarisation can be determined from Bd by taking into consideration the geometric shape of the container in which the gas is placed, the type of gas and its density, and the arrangement of the sensor relative thereto.
If, as is preferred, the container in which the gas is received is spherical in shape, then the magnetic field has a field gradient like that formed by a point dipole.
Thus for a spherical container, the magnetic field Bd of the polarised gas on the equitorial outer surface of the container deriving from the orientated nuclear magnetic dipole moment of the nuclear spin gas is:                               B          d                =                              -            P                    ·          n          ·                                                    R                3                            ⁢                              μ                0                                                    3              ⁢                              r                3                                              ·                      μ            N                                              (        2        )            
where P represents the degree of polarisation to be determined and n the particle density of the gas. The factor R3/3r3 is termed the geometry factor, and depends on the shape of the container and thus on the volume in which the nuclear spin polarised gas is dispersed. R represents the radius of the sphere and r the distance of the sensor from the centre point of the container sphere perpendicular to the dipole axis. xcexc0=1.257xc3x9710xe2x88x926 Vs/Am, i.e. the permeability of vacuum, and xcexcN=1.075xc3x9710xe2x88x9226 Am2, the nuclear dipole moment of the gas (in this case 3He)
Similar equations to equation (2) may be generated for containers which are non-spherical.
The geometric factor also takes the position of the magnetic field measuring apparatus relative to the direction of the magnetic field of the gas into consideration. If the field emerges from the poles of the container, the sensor is positioned in the equatorial plane of the spherical gas container.
Different geometric factors must be used for different container geometries, as in each case there is a different calculable field gradient of magnetic field Bd. If the geometric factor, the distance from the measuring sensor and the particle density of the-nuclear spin polarised gas in the container are known, then equation (2) can be used to determine the absolute degree of polarisation P from the Bd determined using the measuring apparatus.
As an example, assuming a degree of polarisation P=50% and a particle density n=1020/cm3, then the field at the edge of the sphere (r=R) has a value Bd=0.22 xcexcT. This value is of the order of 1 thousandth of the homogeneous magnetic field caused by the polarisation, similar to, for example, transport fields of 0.3 mT, for example, or external stray fields.
In a preferred implementation of the invention, it is proposed that the sensor comprises a very sensitive magnetic field sensor. In this respect, SQUIDs or more preferably sensors operating on the Forster principle can be considered. Fxc3x6rster sensors operate on the principle of saturable-core magnetometers. The measuring element of saturable-core magnetometers essentially consist of one or more narrow cores of highly permeable materials (xcexc-metal or ferrite) with almost linear B(H) behaviour.
In a variation of a saturable-core magnetometer, a double core sensor comprises two mutually parallel cores each provided with a primary and a secondary winding. The former are opposed, the latter are connected in series. The primary winding is supplied with a constant current by means of a low frequency transmitter (xcexd=50 to 1000 Hz). The current intensity is sufficient to magnetise the highly permeable cores to saturation. A voltage is induced in the secondary windings by the changing magnetic field of the primary coils.
With no external magnetic field, the primary fields in the two cores are equal and opposite. Similarly, in the two secondary coils during the time in which the magnetic flux density B changes, equal and opposite voltages are induced, which add up to zero. In the presence of an external field component H0 parallel to the longitudinal axis of the cores, this symmetry shifts by the value of H0. The operating point on the B(H) curve is shifted, and the induced impulses no longer add up to zero, since with a change of H in one core, saturation is achieved faster than in the other. The result is that the voltage pulses of the derivative with time of the flux density dB/dt appear in the two cores at different times. The sum dB1/dt+dB2/dt goes from zero to different signals, the breadth and distance apart in time of which are dependent on the amplitude of the external magnetic field H0 and serve to determine the size of H0.
An example of a commercial sensor which operates using the principle described above is the MAG-03 MS-sensor from Bartington Instruments Ltd.
With such magnetic field sensors, an accuracy of about 5 nT can be achieved in the measurement range B less than 1 mT. Thus it is possible to determine the magnetic field Bd with such sensors.
In order to be able to determine the polarisation- dependent magnetic field Bd of polarised gas in the presence of an applied field B0 (e.g. the ambient field or a substantially uniform generated magnetic field within a transporter device), the polarisation-dependent magnetic field is advantageously determined by displacing the measuring apparatus and container (gas storage cell) relative to each other. This is advantageously achieved in that in a first position as close as possible to the wall of the container containing the nuclear spin polarised gas, a magnetic field sensor is used to record the field value, constituted by the field of the applied field B0 and the field of the nuclear spin polarised gases in the container (Bd at the equatorial plane of the container). After recording this signal the container is moved relative to the sensor to a position distanced from the sensor, preferably in the direction of the axial-applied field, by at least five times the radius of the container. The field component caused by the nuclear spin polarised gas then falls to less than 1% of its original value. This means than in this position only the value of the applied field B0 is measured. The difference between these two signals can be used to determine the value of Bd and thus the degree of polarisation P can be determined using equation (2) given above. It is clearly possible to increase the accuracy of the results obtained for the degree of polarisation using this method by making a series of measurements. In a further embodiment, the magnetic field sensor is displaced from the container. If the applied field B0 changes on displacing the sensor, this must be taken into consideration when calculating the degree of polarization. Moreover if measurement is not made in the equatorial plane of the container, this too must be taken into consideration. Thus if the field is measured in the polar direction of the container, the difference is Bdxe2x80x2=2xc3x97Bd.
These two methods have the advantage that commercially available magnetic field sensors can be used even by inexperienced personnel to determine the magnetic field of the nuclear spin polarised gases to an accuracy of 10%, advantageously 2%. With regard to geometric uncertainties, polarisation determination to 50%, advantageously to  less than 10%, is quite possible.
In a second embodiment of the method of the invention Bd, and hence P, may be determined by using a high frequency magnetic pulse to reverse the polarisation and by measuring the resulting magnetic field change xcex94B without moving the sensor and the container (the gas storage cell) relative to each other.
In this method, the polarisation-dependent magnetic field is advantageously determined by applying a high frequency magnetic pulse over the applied field, so that the sign of P is reversed by nuclear magnetic resonance. To this end, suitable coils or a solenoid are used to emit a high frequency magnetic field pulse of varying amplitude and frequency
B(t)=B1(t).cos(xcfx89(t).t)xe2x80x83xe2x80x83(3)
perpendicular to the applied field B0.
This magnetic field change based on the sign reversal of P preferably occurs on the principle of xe2x80x9cfast adiabatic passagexe2x80x9d, fully described in A. Abragam, xe2x80x9cThe Principles of Nuclear Magnetismxe2x80x9d, Oxford University Press, London, England, 1973 (see especially pages 34-36 and 65-66). In this method, the frequency xcfx89(t) of the high frequency magnetic field pulse during the pulse period is pushed beyond the resonance frequency of the nuclear dipole moment:                               ω          0                =                                            2              ⁢                              πμ                N                                                    h              ⁢                              xe2x80x83                            ⁢                              I                N                                              ·                      B            0                                              (        4        )            
where h is Planck""s constant, and IN is the nuclear spin quantum number. If the pulse period is short and the high frequency field strength Bd (t) is chosen correctly, the polarisation is completely reversed with no reduction in magnitude. This means that the reading of the magnetic field sensor changes by an amount
xcex94B=2Bdxe2x80x83xe2x80x83(5)
In comparison with the method described above, in which the sensor and container are displaced with respect to each other, the method in which the field Bd is determined using a magnetic field pulse has the advantage that a measuring signal xcex94B=2Bd which is twice as large is obtained.
A complete reversal is obtained using the principle of xe2x80x9cfast adiabatic passagexe2x80x9d (see Abragam (supra)) if the following conditions are satisfied as regards emitting a high frequency pulse from a magnetic field pulse transmitter:
1. The applied high frequency magnetic field strength B1 must be large in comparison with the magnetic field variation xcex94B0 which the applied field B0 exhibits because of inhomogeneities in the container dimensions.
2. The frequency shift xcex94xcfx89 between the start and end of the high frequency pulse must be large compared with the broadening of the nuclear resonance lines caused by the field variation xcex94B0.
3. The pulse duration xcex94t must be short compared with the characteristic transverse relaxation time T2of the gas.
4. The product B1. xcex94t must be large compared with hIN/(2ΠxcexcN).
This polarisation reversal method is particularly suitable as a complete polarisation reversal can also be achieved in an extensive gas volume, although the applied field B0 for maintaining the polarisation can vary slightly spatially by xcex94B0. The method is thus robust and guarantees reproducible results, even when the nuclear spin polarised gas container is changed or, for example, external stray fields are superimposed, as may be the case in different locations. The method can advantageously be used in transportable magnetic fields to determine the polarisation of a gas on site even by inexperienced personnel.
A further method of producing a polarisation reversal is to apply a magnetic pulse using the principle of the 180xc2x0 nuclear resonance pulse or xe2x80x9cΠpulsexe2x80x9d, as fully described in A. Abragam (supra) pages 32-34.
In this method, suitable coils or a solenoid are used to produce a high frequency magnetic field pulse of varying amplitude and frequency (equation (3)) perpendicular to the applied field.
For a complete reversal of the nuclear spin polarisation of the gas using the n pulse principle, a magnetic field pulse with frequency xcfx890 (equation (4)) must be applied by a magnetic field pulse transmitter using the following conditions:
1. The applied high frequency magnetic field strength B1 must be large in comparison with the magnetic field variation xcex94B0 which the applied field B0 exhibits because of inhomogeneities in the container dimensions.
2. The pulse duration xcex94t must be short compared with the characteristic transverse relaxation time T2 of the gas.
3. The relationship                               j          ·          π                =                                                            2                ⁢                                  πμ                  N                                                            h                ⁢                                  xe2x80x83                                ⁢                                  I                  N                                                      ·                          B              1                        ·            Δ                    ⁢                      xe2x80x83                    ⁢          t                                    (        6        )            
must be satisfied, where h is Planck""s constant and IN is the nuclear spin quantum number, xcexcN is the nuclear dipole moment of the isotope under consideration, and j=1,3,5,7, etc, however j=1 is normally selected.
In contrast to the xe2x80x9cfast adiabatic passagexe2x80x9d method, in the n pulse method the relationship (6) must hold exactly. This is rendered more difficult if variations xcex94B0 occur in the applied field B0 over the gas volume.
For larger gas volumes, as considered in the present invention, significant field variations xcex94B0 occur over the gas volume so the more robust xe2x80x9cfast adiabatic passagexe2x80x9d method with the particular advantage of complete reversal of the nuclear spin polarisation of the gas is preferred. This does not, however, constitute a limitation of the inventive concept of measuring a polarisation reversal with a magnetic measuring apparatus using nuclear resonance methods.
Viewed from a further aspect, the present invention also provides apparatus for determining the magnetic field (Bd) of a nuclear spin polarised gas (and preferably also for determining the degree of polarisation P thereof), said apparatus comprising a magnetic field sensor arranged to determine the magnetic field at at least two positions relative to a container containing a nuclear spin polarised gas, optionally magnetic field applying means arranged to apply a magnetic field to said container, and optionally computing means for determining the degree of polarisation of the polarised gas from the magnetic fields determined by the sensor.
In this apparatus, the sensor may operate to determine the magnetic fields at the various relative positions or it may simply determine the field difference between the positions.
In the apparatus, the sensor may be movable relative to the container or alternatively it may comprise separate sensors located at different positions relative to the container. The different positions will generally include positions relative closer to and further away from the container. The relative motion of sensor and container may be achieved by moving sensor and/or container to preset receiving sites or along a guide, e.g. using a drive means (for example a motor-driven or hand operated drive means)
In this apparatus, the means for applying a magnetic field are preferably means, e.g. a permanent or electromagnet, for applying a substantially uniform field Bo.
Viewed from an alternative aspect the invention also provides apparatus for determining the magnetic field (Bd) of a nuclear spin polarised gas (and preferably also for determining the degree of polarisation (P) of the gas), said apparatus comprising a magnetic field sensor and means for applying a time variant magnetic field to a container containing a nuclear spin polarised gas, optionally also means for applying a substantially uniform magnetic field to said container, and optionally computing means for determining the degree of polarisation of the polarised gas from the magnetic field variation determined by the sensor.
In this second form of apparatus according to the invention, there may if desired be two or more sensors and the sensor and container may be movable relative to each other.
In both forms of the apparatus of the invention the container is preferably spherical and the sensors are preferably highly sensitive, e.g. SQUIDs or Forster principle magnetometers.
The first apparatus of the invention thus conveniently comprises apparatus for determining the degree of polarisation (P) of nuclear spin polarised gases in which the nuclear spin polarised gas is placed in a container, the apparatus comprising: at least one highly sensitive magnetic field sensor, wherein the sensor and the container are arranged so as to be displaceable relative to each other, so that the magnetic field can be determined in at least two locations, e.g. one close to and one distanced from the container, and thus the magnetic field Bd can be determined.
The second apparatus of the invention also conveniently comprises apparatus for determining the degree of polarisation (P) of nuclear spin polarised gases in which the nuclear spin polarised gas is placed in a container, the apparatus comprising: at least one highly sensitive magnetic field sensor, and a high frequency magnetic field pulse transmitter arranged to emit a high frequency magnetic field pulse of variable amplitude and frequency.
The apparatus of the invention is desirably incorporated into apparatus for transporting hyperpolarised gases in which the container is placed within an area of highly uniform applied magnetic field in a chamber within the transporter apparatus.
In a special embodiment, the high frequency magnetic field pulse transmitter comprises coils or solenoids. In one particular embodiment, the magnetic field pulse transmitter is constructed so that a magnetic field pulse is emitted by which the polarisation is completely reversed with no reduction in magnitude.
The use of the apparatus and method of the invention are particularly advantageous with respect to the prior art for the following reasons:
Commercially available apparatus components (e.g. sensors) with high precision and with reproducible results with a relative error of only 0.5% or less can be used. These commercially available apparatus components are calibrated so expensive calibration can be avoided.
The prior art methods for determining the nuclear spin polarisation which induce small nuclear resonance excitations are based on recording the dynamic nuclear spin resonance signal thus produced, recorded with a receiver apparatus. A very costly calibration is necessary for absolute polarisation determination, in which very small resonance signals are measured, which are very sensitive to disturbances from external influences such as container geometry or the construction of the receiver apparatus. In order to produce good results, each receiver apparatus must be separately calibrated, and that calibration is only valid for one container geometry. Using a magnetic field sensor as in the invention means that the very expensive calibration of the receiver apparatus and standardisation of the container geometry is no longer required. The influence of container geometry can be readily calculated. The static magnetic field of the nuclear spin polarised gas is measured. Then a series of measurements of the static magnetic field before and after polarisation reversal can be made to substantially increase the accuracy of the method. The measuring method can thus advantageously be embodied in a measuring apparatus. The measuring apparatus itself is highly reproducible and reliable. In particular, the measuring method is also suitable for use by inexperienced personnel because of its robustness.